Question 1

How would you translate the phrase 'twice y is added to 4'?

Accepted Answer

Answer

Answer

Answer

Question 2

Translate the phrase 'The product of a number n and 7, decreased by 12' into a mathematical expression.

Accepted Answer

Answer

Answer

Answer

Question 3

Translate the statement 'Three more than half of a number x equals five' into a mathematical equation.

Accepted Answer

Answer

Answer

Answer

Question 4

If a phrase states 'The difference between twice a number y and seven is equal to ten', how would you express this as an equation?

Accepted Answer

Answer

Answer

Answer

Question 5

Translate the sentence 'Four times a number z decreased by three is equal to fifteen' into a mathematical equation.

Accepted Answer

Answer

Answer

Answer

Question 6

How would you translate the expression 'The sum of three times a number x and eight is equal to twenty' into an equation?

Accepted Answer

Answer

Answer

Answer

Question 7

Translate the statement 'Five less than thrice a number k equals eleven' into a mathematical equation.

Accepted Answer

Answer

Answer

Answer

Question 8

How would you express the phrase 'Seven added to twice a number m equals nineteen' as a mathematical equation?

Accepted Answer

Answer

Answer

Answer

Question 9

Which of the following expressions translates the phrase 'the product of 7 and a number x increased by 5' into a mathematical equation?

Accepted Answer

Answer

Answer

Answer

Question 10

Translate the mathematical expression

3(y - 4)

into words.

Accepted Answer

Three times the difference of y and 4

Answer

Three added to the difference of y and four

Answer

Three plus the difference of y and 4

Answer

Three times y minus four

Question 11

Which expression corresponds to the phrase 'the square of a number z minus twice the number'?

Accepted Answer

Answer

Answer

Answer

Question 12

Which expression represents 'twice the sum of a number x and 5 is equal to 20'?

Accepted Answer

Answer

Answer

Answer

Question 13

Translate the equation

3(y - 4)

into words.

Accepted Answer

Four times a number n plus nine equals thirty-three

Answer

Four plus nine times a number n equals thirty-three

Answer

Four times the sum of a number n and nine equals thirty-three

Answer

The sum of four and a number n plus nine equals thirty-three

Question 14

Which expression can be used to represent the phrase 'the sum of twice a number m and 8 is equal to 18'?

Accepted Answer

Answer

Answer

Answer

Question 15

How would you express 'five less than the product of 3 and a number y' as a mathematical expression?

Accepted Answer

Answer

Answer

Answer

Question 16

Which of the following represents an existential statement?

Accepted Answer

There exists a student in the class who has completed the assignment.

Answer

Every student in the class does not understand the topic.

Answer

All students in the class have completed the assignment.

Answer

No students in the class are aware of the exam.

Question 17

Which of the following is an example of a quantifier?

Accepted Answer

For all

Answer

Sometimes

Answer

Maybe

Answer

Often

Question 18

What does the statement 'Some cats are not playful' represent?

Accepted Answer

An existential statement

Answer

A tautology

Answer

A contradiction

Answer

A universal statement

Question 19

Which of the following correctly indicates a universal quantifier?

Accepted Answer

For every x, P(x)

Answer

Some x are not P

Answer

At least one x must be P

Answer

There exists an x such that P(x)

Question 20

What is the meaning of the statement 'There exists an integer n such that n > 5'?

Accepted Answer

There is at least one integer greater than 5.

Answer

No integers are greater than 5.

Answer

Every integer is less than or equal to 5.

Answer

All integers are greater than 5.

Question 21

Which of the following correctly represents the existential statement 'Not all cars are electric'?

Accepted Answer

There exists at least one car that is not electric.

Answer

No car is electric.

Answer

Every car is electric.

Answer

All cars are electric.

Question 22

Which of the following statements is true regarding quantifiers?

Accepted Answer

The statement 'For every x, P(x)' implies that P(x) is true for all x.

Answer

The statement 'For every x, P(x)' is equivalent to 'There exists an x such that P(x)'.

Answer

The statement 'There exists an x such that P(x)' means P(x) is false for all x.

Answer

The statement 'Some x are not P' implies P is true for all x.

Question 23

What is the proper translation of the logical statement 'Some dogs bark'?

Accepted Answer

There exists at least one dog that barks.

Answer

Every dog barks.

Answer

All dogs bark.

Answer

No dogs bark.

Question 24

What is the correct translation of the universal statement 'All birds can fly'?

Accepted Answer

For every bird, it can fly.

Answer

No birds can fly.

Answer

There exists a bird that can fly.

Answer

Some birds cannot fly.

Question 25

Which of the following statements is a universal statement?

Accepted Answer

All humans are mortal.

Answer

There exists a human who is not mortal.

Answer

Most humans are mortal.

Answer

Some humans are mortal.

Question 26

Which of the following statements correctly translates to 'There exists an x such that P(x) is true'?

Accepted Answer

∃x P(x)

Answer

¬∃x P(x)

Answer

P(x) is true for all x

Answer

∀x P(x)

Question 27

If the statement 'No dogs bark' is represented logically, which of the following is its correct form?

Accepted Answer

∀x (Dog(x) → ¬Bark(x))

Answer

∃x (Dog(x) → Bark(x))

Answer

∃x (Dog(x) ∧ Bark(x))

Answer

∀x (Dog(x) ∧ Bark(x))

Question 28

Which of the following represents an existential statement?

Accepted Answer

There is a student who enjoys mathematics.

Answer

All students enjoy mathematics.

Answer

Every student must enjoy mathematics.

Answer

No students enjoy mathematics.

Question 29

In logical terms, which phrase best represents the universal quantifier?

Accepted Answer

For all

Answer

There exists

Answer

Some

Answer

At least one

Question 30

Which of the following statements is true when using the universal quantifier?

Accepted Answer

For every number x, x + 1 is greater than x.

Answer

There exists a number x such that x + 1 is equal to x.

Answer

For some numbers x, x + 1 is less than x.

Answer

There is no number x such that x + 1 > x.

Question 31

What is the negation of the statement 'All cats are white'?

Accepted Answer

There exists a cat that is not white.

Answer

Every cat is white or black.

Answer

All cats are not white.

Answer

No cats are white.

Question 32

Which quantifier indicates that a property holds for at least one element in a set?

Accepted Answer

Existential quantifier

Answer

Universal existence

Answer

Universal quantifier

Answer

Universal negation

Question 33

Which of the following is the correct translation of the statement 'For every x, there exists a y such that P(x, y)'?

Accepted Answer

∀x ∃y P(x, y)

Answer

∀x ∀y P(x, y)

Answer

∃x ∃y P(x, y)

Answer

∃x ∀y P(x, y)

Question 34

What is the universal quantifier used to express that a property is true for all elements in a set?

Accepted Answer

For all

Answer

Some

Answer

At least one

Answer

There exists

Question 35

Which of the following statements is an existential statement?

Accepted Answer

There exists at least one student who passed the exam.

Answer

No students passed the exam.

Answer

Every student will pass the exam.

Answer

All students passed the exam.

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